Crooked Timber

I was rereading Bill Lycan’s paper On the Gettier Problem Problem and I noticed a couple of odd things about his view that knowledge justified true belief with ‘no false assumptions’. I think Lycan does a pretty good job in arguing that the cases that were traditionally thought to pose a problem for this view do not really pose such a problem. But still there are three kinds of cases where I think something needs to be said.
First, it seems to me much too strong to rule out all cases of inference from false premise. It doesn’t seem plausible to say that an engineer doesn’t know his bridge will stand up because he presupposed a little bit of Newtonian theory in his calculations. This is a fairly well known case and I think people generally think there’s a fairly easy fix. (Take the assumption not to be the perfect accuracy of Newtonian theory, but the approximate accuracy, and now the assumptions the engineer makes are all true.) But I suspect the problem here is much more general than this one case, and the solution won’t in fact generalise.

For a striking case, consider Kevin Davey’s discussion in the British Journal for the Philosophy of Science of path integrals, as introduced by Feynman. We know there is some false assumption going on here, because the mathematical theory is contradictory. It seems to turn out that provided we are careful with how we apply the theory, provided we are ‘inferentially restrictive’ in Davey’s terminology, we avoid contradictory results. I’d even say that we gain knowledge this way. The difficulty is that no one knows what a consistent (let alone true) mathematical theory that does the work path integrals currently do might look like, certainly no one knows how to replace the theory with a true version, and it doesn’t look (at least to me) like this is a case where the theory we use is in any sense an approximation to the theory that is true. (Could a contradictory theory approximate the true theory?) Either we have to say that the physicists here are not getting knowledge about the world, or we have to put quite sharp limits on what we say about inference from a false premise.

For a second worry, consider a case where I’m in a state that we’d usually call a paradigmatic instance of knowing that p, but I also have some false belief that q. Presumably the fact that in learning that p I acquire the false belief that p & q doesn’t mean I fail to know p. But it isn’t clear why this doesn’t follow on Lycan’s theory.

Finally, there seem to be really difficult cases of existential Nogot which require quite a bit of fancy footwork. Here are two.

Testimonial Nogot
A acquires a justified false belief that Smith owns a Ford. In fact Smith’s workmate Jones owns a Ford, but A’s only reason for believing that someone in the office owns a Ford is that he believes Smith owns a Ford. B asks A, what brands of car are owned by people in the office, and A says “Holden and Ford.” B comes to truly believe that someone in the office owns a Ford.

I guess the false assumption there is that A knows that someone in the office owns a Ford.

Faulty Machine
A machine at the front door of the office measures whether anyone going in is over 2 metres tall, and a light goes on if that is the case. (The light goes off at the end of each day.) Smith, who is just under 2 metres tall, walks in and the machine malfunctions, measuring him as over 2 metres tall, and lights up. Jones, who is over 2 metres tall, walks in through the back door. A sees the light and infers that someone in the office is over 2 metres tall.

Here I think the false assumption is that the person who caused the light to turn on is over 2 metres tall. But note that this implies a lack of knowledge in the following case.

Faulty Machine part II
A machine at the front door of the office measures whether anyone going in is over 2 metres tall, and a light goes on if that is the case. (The light goes off at the end of each day.) Smith, who is just under 2 metres tall, walks in and the machine malfunctions, measuring him as over 2 metres tall, and lights up. Just after that Jones, who is over 2 metres tall, walks in through the front door, and he would have caused the light to go on if Smith had not. A sees the light and infers that someone in the office is over 2 metres tall.

It seems a little wrong to me to deny knowledge in that case, but I’m not sure how a theory like Lycan’s can distinguish the two.

The reason for all this is that the tweaks I’m using to turn my theory of justified belief into a theory of knowledge bear a strong resemblence to Lycan’s theory of knowledge, so any bugs in his theory might be replicated in mine. So it’s find ‘em and exterminate time around here!

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3 Responses to “Knowledge and False Beliefs”

jon kvanvig says:

Brian, depending on what else is true of the machine, I’m not sure there is a difference between the two faulty machine cases. As you describe the machine, it appears to be one that is reliable for detecting tall people, but not great at avoiding false positives. If that’s accurate, then I don’t think it matters whether Jones comes in the front door or the back door.

The alternative is that there was a bizarre power surge that caused a unique interruption of the ordinary operation of the machine, so that the machine, when operating under normal conditions, doesn’t generate false positives. Then the problem is the central problem for the defeasibility theory: distinguishing misleading from non-misleading defeaters.

This is a pleasing result, to my mind: Lycan wants to avoid the muck and mire of the defeasibility literature, but ends up there anyway! Unless, of course, he’s willing to bite the big one and say that the cases are symmetrical with respect to knowledge.
I guess I’d like it if your JTB alternative faced the same pleasing dilemma—just when you thought you it was safe to go out, the very issue that undermines attempts to defend the value of knowledge plagues theories that try to avoid the Gettier problem, too!

I don’t know enough details of the path integral case to be very confident in this answer, but from the description you put forward, it seems like we can say the following:

There’s no false assumption involved in using path integrals. Physicists know that the mathematical theory of path integrals is contradictory, but they also know that if you use path integrals in a very specific way, then you don’t get entangled in the contradictions and you get results that are reliable. So long as the physicists think of what they’re doing that way, there’s no false assumption involved. Another possibility is that some physicists who don’t know the conditions under which path integrals work accept that they can use path integrals based on testimony. If, on the other hand, the physicists were making the assumption that path integrals were consistent, without checking that they’d get the right results regardless, then they’ve got an essential false assumption, and I’m not sure it’s counter-intuitive to deny them knowledge.

I assume you’re making the point that in II, if the false positive hadn’t occurred, then Jones would have triggered the light anyway, and A’s inference clearly would have been knowledge. That’s true, but the fact is that the false positive did occur, and that’s enough to break A’s chain of reasoning (since A assumes the machine functioned correctly). That events thereafter luckily conspire to make A’s belief true and justified don’t change that, and can’t be considered relevant to whether A has knowledge or not. Those events merely make it appear that A has knowledge. A’s belief being true is due to luck (i.e., that Jones subsequently happened to walk through the front door), not to a valid chain of reasoning. So A’s belief is not knowledge.